Percival Hygiene has $$10$ million invested in long$-$term corporate bonds. This bond portfolio's expected annual rate of return is $11\%,$ and

the annual standard deviation is $12\%.$ Amanda Reckonwith, Percival's financial adviser, recommends that Percival consider investing in

an index fund that closely tracks the Standard & Poor's $500$ index. The index has an expected return of $16\%,$ and its standard deviation

is $17\%.$

a$.$ Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he thereby improve his expected rate

of return without changing the risk of his portfolio? The Treasury bill yield is $6\%.$

Yes

No

b$.$ Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation

between the bond portfolio and the index fund is $+0\mathrm{.}3.$

Yes

No